The leading shock in a steady shock train takes one of two forms: oblique or normal. However, the phenomenon and mechanism of the normal-to-oblique transition of the leading shock in a forced shock train have not been widely reported. In this study, leading normal and oblique shocks are experimentally observed at the same position and similar velocities in a forced oscillation shock train with an incoming Mach number of 1.83. The normal-to-oblique transition is found to be closely related to the self-excited oscillation of the shock train. In addition, we find that the direct use of free-interaction theory cannot accurately predict the leading shock angle in a moving shock train. Thus, free-interaction theory requires appropriate correction for this scenario.
REFERENCES
1.
K.
Matsuo
,
Y.
Miyazato
, and
H.
Kim
, “
Shock train and pseudo-shock phenomena in internal gas flows
,” Prog. Aerosp. Sci
35
, 33
–100
(1999
).2.
H.
Zare-Behtash
,
K. H.
Lo
,
K.
Kontis
,
T.
Ukai
, and
S.
Obayashi
, “
Transverse jet-cavity interactions with the influence of an impinging shock
,” Int. J. Heat Fluid Flow
53
, 146
(2015
).3.
T.
Ukai
,
H.
Zare-Behtash
,
K. H.
Lo
,
K.
Kontis
, and
S.
Obayashi
, “
Effects of dual jets distance on mixing characteristics and flow path within a cavity in supersonic crossflow
,” Int. J. Heat Fluid Flow
50
, 254
(2014
).4.
T.
Ukai
,
H.
Zare-Behtash
,
E.
Erdem
,
K. H.
Lo
,
K.
Kontis
, and
S.
Obayashi
, “
Effectiveness of jet location on mixing characteristics inside a cavity in supersonic flow
,” Exp. Therm. Fluid Sci.
52
, 59
–67
(2014
).5.
F.
Gnani
,
B. H.
Zare
, and
K.
Kontis
, “
Pseudo-shock waves and their interactions in high-speed intakes
,” Prog. Aerosp. Sci.
82
, 36
–56
(2016
).6.
A. C.
Idris
,
M. R.
Saad
,
B. H.
Zare
, and
K.
Kontis
, “
Luminescent measurement systems for the investigation of a scramjet inlet-isolator
,” Sensors
14
, 6606
(2014
).7.
F.
Gnani
,
H.
Zare-Behtash
,
C.
White
, and
K.
Kontis
, “
Numerical investigation on three-dimensional shock train structures in rectangular isolators
,” Eur. J. Mech. -B/Fluids
72
, 586
–593
(2018
).8.
Y.
Miyazato
,
K.
Matsuo
, and
R.
Kasada
, “
Experimental and theoretical investigations of normal shock wave/turbulent boundary-layer interactions at low Mach numbers in a square straight duct,” in
Proceedings of 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
(
American Institute of Aeronautics and Astronautics
,
Orlando, Florida
, 2009
), p. 925
.9.
R. L.
Klomparens
,
J. F.
Driscoll
, and
M.
Gamba
, “
Boundary layer separation in a 3D shock train
,” AIAA Paper No. AIAA 2015-1519, 2009
.10.
R. L.
Hunt
and
M.
Gamba
, “
Shock train unsteadiness characteristics, oblique-to-normal transition, and three-dimensional leading shock structure
,” AIAA J.
56
, 1569
(2018
).11.
V. R. P.
Sethuraman
,
Y.
Yang
, and
J. G.
Kim
, “
Low-frequency shock train oscillation control in a constant area duct
,” Phys. Fluids
34
, 016105
(2022
).12.
N.
Li
, “
Reciprocating and flapping motions of unstart shock in a scramjet isolator
,” Phys. Fluids
34
(1
), 016102
(2022
).13.
Z. A.
Wang
,
J. T.
Chang
,
G. W.
Wu
, and
D. R.
Yu
, “
Experimental investigation of shock train behavior in a supersonic isolator
,” Phys. Fluids
33
, 046103
(2021
).14.
Z. A.
Wang
,
J. T.
Chang
,
Y. M.
Li
et al, “
Oscillation of the shock train under synchronous variation of incoming Mach number and backpressure
,” Phys. Fluids
34
, 046104
(2022
).15.
Z. A.
Wang
,
J. T.
Chang
,
W. X.
Hou
, and
D. R.
Yu
, “
Low-frequency unsteadiness of shock-wave/boundary-layer interaction in an isolator with background waves
,” Phys. Fluids
32
, 056105
(2020
).16.
T.
Ikui
,
K.
Matsuo
,
M.
Nagai
, and
M.
Honjo
, “
Oscillation phenomena of pseudo-shock waves
,” Bull. JSME
17
, 1278
(1974
).17.
R.
Yamane
,
E.
Kondo
,
Y.
Tomita
, and
N.
Sakae
, “
Vibration of pseudo-shock in straight duct: 1st report, fluctuation of static pressure
,” Bull. JSME
27
, 1385
(1984
).18.
R.
Yamane
,
M.
Takahashi
, and
H.
Saito
, “
Vibration of pseudo-shock in straight duct: 2nd report, calculation of static pressure fluctuation
,” Bull. JSME
27
, 1393
(1984
).19.
H.
Sugiyama
,
H.
Takeda
,
J.
Zhang
,
K.
Okuda
, and
H.
Yamagishi
, “
Locations and oscillation phenomena of pseudo-shock waves in a straight rectangular duct
,” JSME Int. J. Ser. 2, Fluids Eng. Heat Transfer, Power, Combust., Thermophys. Prop.
31
, 9
–15
(1988
).20.
R. L.
Hunt
and
M.
Gamba
, “
On the origin and propagation of perturbations that cause shock train inherent unsteadiness
,” J. Fluid Mech.
861
, 815
(2019
).21.
K.-C.
Lin
,
K.
Jackson
,
R.
Behdadnia
,
T. A.
Jackson
,
M.
Jackson
,
F. H.
Ma
, and
V.
Yang
, “
Acoustic characterization of an ethylene-fueled scramjet combustor with a rectangular cavity flameholder
,” J. Propul. Power
26
, 5382
(2007
).22.
S.
Laurence
,
S.
Karl
,
J.
Schramm
, and
K.
Hannemann
, “
Transient fluid-combustion phenomena in a model scramjet
,” J. Fluid Mech.
722
, 85
–120
(2013
).23.
Y.
Tian
,
Y.
Han
,
S.
Yang
,
F.
Zhong
, and
J.
Le
, “
Investigation of fluctuating characteristics of wall shear stress in supersonic flow
,” Phys. Fluids
31
, 125110
(2019
).24.
Y.
Tian
,
W.
Shi
,
F.
Zhong
, and
J.
Le
, “
Pilot hydrogen enhanced combustion in an ethylene-fueled scramjet combustor at Mach 4
,” Phys. Fluids.
33
, 015105
(2021
).25.
F.
Gnani
,
H.
Zare-Behtash
,
C.
White
, and
K.
Kontis
, “
Effect of back-pressure forcing on shock train structures in rectangular channels
,” Acta Astronaut.
145
, 471
–481
(2018
).26.
B.
Xiong
,
X. Q.
Fan
,
Z. G.
Wang
, and
Y.
Tao
, “
Analysis and modelling of unsteady shock train motions
,” J. Fluid Mech.
846
, 240
(2018
).27.
R.
Saravanan
,
S. L. N.
Desikan
, and
T. M.
Muruganandam
, “
Isolator characteristics under steady and oscillatory back pressures
,” Phys. Fluids
32
, 096104
(2020
).28.
L. M.
Edelman
,
M.
Gamba
,
R.
Hunt
,
A.
Auslender
,
J. M.
Donbar
, and
M.
Hagenmaier
, “
Application of flux-conserved modeling to an unsteady combustion driven pseudo-shock
,” AIAA Paper No. AIAA 2021-1763, 2021
.29.
B.
Xiong
,
X.-Q.
Fan
,
Y.
Wang
, and
Y.
Tao
, “
Experimental study on self-excited and forced oscillations of an oblique shock train
,” J. Spacecr. Rockets
55
, 640
–647
(2018
).30.
C.
Cheng
,
C.
Wang
, and
K.
Cheng
, “
Response of an oblique shock train to downstream periodic pressure perturbations
,” Proc. Inst. Mech. Eng., Part G
233
, 57
–70
(2019
).31.
B.
Xiong
,
Z. G.
Wang
,
X. Q.
Fan
, and
Y.
Wang
, “
Response of shock train to high-frequency fluctuating backpressure in an isolator
,” J. Propul. Power
33
, 1520
(2017
).32.
H.
Babinsky
and
J. K.
Harvey
, Shock Wave-Boundary-Layer Interactions
(
Cambridge University Press
, 2011
), pp. 41
–53
.33.
W.-Z.
Xie
,
S.-Z.
Yang
,
C.
Zeng
,
K.
Liao
,
R.-H.
Ding
,
L.
Zhang
, and
S.
Guo
, “
Improvement of the free-interaction theory for shock wave/turbulent boundary layer interactions
,” Phys. Fluids
33
, 075104
(2021
).34.
H.
Chen
,
Q.-Z.
Zhang
,
W.-H.
Luo
, and
L.-J.
Yue
, “
Switching between symmetric and asymmetric separation-induced shock reflections in an oscillatory duct flow
,” Phys. Fluids
34
, 071703
(2022
).35.
F. M.
White
, Viscous Fluid Flow
, 2nd ed
. (
McGraw-Hill
,
New York
, 1991
), pp. 158
–159
.36.
A.
Kendall
and
M.
Koochesfahani
, “
A method for estimating wall friction in turbulent wall-bounded flows
,” Exp. Fluids
44
, 773
–780
(2008
).37.
D. R.
Chapman
,
D. M.
Kuehn
, and
H. K.
Larson
, “
Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition
,” Report No. NACA-TR-1356
(National Advisory Council for Aeronautics, 1956
).38.
J.
Erdos
and
A.
Pallone
, “
Shock-boundary layer interaction and flow separation
,” in Proceedings of the Heat Transfer and Fluid Mechanics Institute
, 1962
.39.
P. J. K.
Bruce
and
H.
Babinsky
, “
Unsteady shock wave dynamics
,” J. Fluid Mech.
603
, 463
(2008
).40.
N.
Li
,
J.-T.
Chang
,
K.-J.
Xu
,
D.-R.
Yu
,
W.
Bao
, and
Y.-P.
Song
, “
Prediction dynamic model of shock train with complex background waves
,” Phys. Fluids
29
, 116103
(2017
).41.
P. S. R.
Touré
and
E.
Schülein
, “
Scaling for steady and traveling shock wave/turbulent boundary layer interactions
,” Exp. Fluids
61
, 156
(2020
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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